Exam 7: Asset Pricing Models: Capm and Apt

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Calculate the expected return for E Services which has a beta of 1.5 when the risk free rate is 0.05 and you expect the market return to be 0.11.

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Exhibit 7-8 USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S) Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas) Stack Factor 1 Loading Factor 2 Loading -0.55 1.2 -0.10 0.85 0.35 0.5 The zero-beta return (λ₀) = 3%, and the risk premia are λ₁ = 10%, λ₂ = 8%. Assume that all three stocks are currently priced at $50. -Refer to Exhibit 7-8. The expected prices one year from now for stocks X, Y, and Z are

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Findings by Fama and French that stocks with high Book Value to Market Price ratios tended to produce larger risk adjusted returns than stocks with low Book Value to Market Price ratios challenge the efficacy of the CAPM.

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Exhibit 7-8 USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S) Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas) Stack Factor 1 Loading Factor 2 Loading -0.55 1.2 -0.10 0.85 0.35 0.5 The zero-beta return (λ₀) = 3%, and the risk premia are λ₁ = 10%, λ₂ = 8%. Assume that all three stocks are currently priced at $50. -Refer to Exhibit 7-8. Assume that you wish to create a portfolio with no net wealth invested and the portfolio that achieves this has 50% in stock X, -100% in stock Y, and 50% in stock Z. What is the net arbitrage profit?

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The line of best fit for a scatter diagram showing the rates of return of an individual risky asset and the market portfolio of risky assets over time is called the

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Studies have shown the beta is more stable for portfolios than for individual securities.

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Exhibit 7-6 USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S) Jonathan Crowley is a portfolio manager for a large pension fund. Last year his portfolio had an actual return of 12.6% with a standard deviation of 13% and a beta of 1.3. The market risk premium for this period of time was 6% and the risk-free rate of return was 5%. -Refer to Exhibit 7-6. Based on the Capital Asset Pricing Model (CAPM), what is the required rate of return for this portfolio?

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Consider a two-factor APT model where the first factor is changes in the 30-year T-bond rate, and the second factor is the percent growth in GNP. Based on historical estimates you determine that the risk premium for the interest rate factor is 0.02, and the risk premium on the GNP factor is 0.03. For a particular asset, the response coefficient for the interest rate factor is -1.2, and the response coefficient for the GNP factor is 0.80. The rate of return on the zero-beta asset is 0.03. Calculate the expected return for the asset.

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Calculate the expected return for D Industries which has a beta of 1.0 when the risk free rate is 0.03 and you expect the market return to be 0.13.

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Exhibit 7-9 USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S) Stocks A, B, and C have two risk factors with the following beta coefficients. The zero-beta return (λ0) = .025 and the risk premiums for the two factors are (λ1) = .12 and (λ0) = .10. Stock Factor 1 Factor 2 A -0.25 1.1 B -0.05 0.9 C 0.01 0.6 -Refer to Exhibit 7-9. Calculate the expected returns for stocks A, B, C. I. 0.082 0.091 0.033 II. 0.105 0.109 0.032 III. 0.132 0.128 0.033 IV. 0.165 0.121 0.032 V. 0.850 0.850 0.610

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Beta is a measure of unsystematic risk.

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Unlike the capital asset pricing model, the arbitrage pricing theory requires only the following assumption(s):

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Using the S&P/TSX composite index as the proxy market portfolio when evaluating a portfolio manager relative to the SML will tend to underestimate the manager's performance.

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The capital market line is the tangent line between the risk free rate of return and the efficient frontier.

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Exhibit 7-2 USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S) You expect the risk-free rate (RFR) to be 3% and the market return to be 8%. You also have the following information about three stocks. STOCK BETA CURRENT PRICE EXPECTED PRICE EXIPECTED DIVIDEND 1.25 \ 20 \ 23 \ 1.25 1.50 \ 27 \ 29 \ 3.25 0.90 \ 35 \ 38 \ 1.00 -Refer to Exhibit 7-2. What are the expected (required) rates of return for the three stocks (in the order X, Y, Z)?

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The market portfolio consists of all risky assets.

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Exhibit 7-4 USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S) Stock Beta Current Price Expected Price Expected Dividend 0.8 \ 12.50 \ 13.10 \ 0.80 1.1 \ 8.25 \ 9.76 \ 0.20 2.1 \ 25.70 \ 30.04 \ 0.00 -Refer to Exhibit 7-4. If the expected return on the market is 11.5% and the risk-free rate of return is 4.5%, then what are the required rates of return for stocks X, Y, and Z based on the CAPM? I. 4.8\% 18.3\% 16.9\% II. 7.2\% 20.7\% 22.3\% III. 10.7\% 17.5\% 14.4\% IV. 10.1\% 12.2\% 19.2\% V. 11.1\% 12.2\% 21.3\%

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The planning period for the CAPM is the same length of time for every investor.

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As the number of securities in a portfolio increases, the amount of systematic risk

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Exhibit 7-7 USE THE FOLLOWING INFORMATION FOR THE NEXT QUESTION(S) (1) Capital markets are perfectly competitive. (2) Quadratic utility function. (3) Investors prefer more wealth to less wealth with certainty. (4) Normally distributed security returns. (5) Representation as a K factor model. (6) A market portfolio that is mean-variance efficient. -Refer to Exhibit 7-7. Which are not assumptions of the Arbitrage Pricing model?

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